Nurturing Successful Mathematicians
The Strands of Mathematical Proficiency model introduced by Kilpatrick et al (2001) has informed the way we design NRICH tasks, and we often use it in professional development workshops with teachers, drawing attention to the importance of a balanced curriculum which develops all five strands of students' mathematical proficiency equally, rather than promoting some strands at the expense of others.
We have developed a model and image which uses child-friendly language, so that teachers and parents can share with students five key ingredients that characterise successful mathematicians. At NRICH, we believe that learning maths is about much more than just learning topics and routines. Successful mathematicians understand the curriculum content and are fluent in mathematical skills and procedures, but they can also solve problems, explain their thinking and have a positive attitude about themselves as learners of mathematics.
Understanding - Maths is a network of linked ideas. I can connect new mathematical thinking to what I already know and understand.
Tools - I have a toolkit that I can choose tools from to help me solve problems. Practising using these tools helps me become a better mathematician.
Problem solving - Problem solving is an important part of Maths. I can use my understanding, skills and reasoning to help me work towards solutions.
Reasoning - Maths is logical. I can convince myself that my thinking is correct and I can explain my reasoning to others.
Attitude - Maths makes sense and is worth spending time on. I can enjoy Maths and become better at it by persevering.
At NRICH, we want learners to appreciate that there are many ways to demonstrate their mathematical capabilities, and to recognise the ways in which they behave mathematically. You may be interested to read What We Think and Why We Think It to find out more about the research that informs our thinking and the development of our resources. Perhaps most importantly, we want learners to feel positive about themselves as learners of mathematics. The article Getting into and staying in the Growth Zone makes the case that resilience is the key to tackling anxiety about mathematics.
With this in mind, we have created this self assessment tool to help learners recognise where their mathematical strengths and weaknesses lie. All of the activities in the accompanying features are designed to offer learners opportunities to develop their mathematical capabilities in multiple strands. We hope learners will have a go at some of the activities and then take time to reflect on their own mathematical capabilities.
Ref: Kilpatrick, J., Swafford, J. and Findell, F. (eds) (2001) Adding It Up: Helping Children Learn Mathematics. Mathematics Learning Study Committee: National Research Council.